Human error risk prioritization in crane operations based on CPT and ICWGT

Human error plays a significant role in crane safety. To increase the accuracy and rationality of human error risk prioritization for crane operations, this study proposes a risk prioritization model for human errors in crane operations based on the cumulative prospect theory (CPT) and the improved combination weighting model of game theory (ICWGT). The ICWGT integrates the risk-factor weights obtained via subjective and objective methods. Trapezoidal fuzzy numbers are used to describe experts’ uncertainty information. Then, the CPT is applied to handle the assessment of experts’ risk attitudes in the decision process. The human error risk ranking of crane operations is obtained according to the overall prospect values calculated using the CPT. A case study of human error in overhead crane operations was conducted, and sensitivity and comparison analyses confirmed the feasibility of the proposed model. The proposed ranking mechanism for human error risk priority in crane operations is helpful for crane risk management.


Introduction
Cranes are widely used in construction, dockyards, railway transportation, and other production fields for heavy load hoisting and conveying [1].In 2021, 2.73 million cranes were registered in China [2].Crane accidents account for a large proportion of accidents involving special equipment [3,4].In 2021, 110 special-equipment accidents were reported in China, killing 99 people, of which crane accidents accounted for 26.36% [2] and were responsible for 30.3% of the total deaths [2].As shown in Fig 1, crane accidents and death tolls exhibit a descending trend.However, crane safety remains an important issue in China.Between 2017 and 2021, 322 workers died in 275 crane-related accidents in China, with an average of 65 deaths per year.The average death toll was 51% higher than that in the United States from 1992 to 2006 [5].Thus, the analysis of crane safety and risk is vital for preventing accidents and reducing casualties.
Cranes encounter several potential risk factors during the manufacturing process, such as structural deformation [6], human error [7], and fracture [8].These risk factors may result in casualties, severe economic losses, and other adverse social effects.The main cause of crane accidents is improper and illegal human operations [2].Thus, human error during operations plays an important role in crane safety analyses [7].Analysis of failure risk is a crucial part of studying process safety to identify key failure paths, investigate potential risk factors, and ensure safe operations.Therefore, risk analysis of human error in crane operations is crucial for safe production.
Failure mode and effects analysis (FMEA) has been used in various fields [9].It can prioritize potential failure modes for safety management and assign a risk priority number (RPN) as an index for evaluating the risk level of each failure mode.The RPN is determined by multiplying three factors: occurrence (O), severity (S), and detection (D) [10].For example, to address the complex problems of a quayside container crane system, Zhang et al. [11] proposed a health monitoring method based on FMEA.Sun et al. [12] applied the fuzzy FMEA and ALARP (as low as a reasonably practical rule) methods to rank the potential risks of ship-toshore container crane heightening.Although traditional FMEA methods have the advantages of simplicity and clarity, their limitations have attracted increasing attention.The most significant results are summarized below [13].(1) The rationality of the RPN calculation is debatable.
(2) The same RPN can be achieved using different combinations of O, S, and D, which is inconvenient for risk management.(3) It may be difficult to determine the precise values of O, S, and D. (4) The relative importance of these three risk factors is generally neglected.
In response to these deficiencies, many multi-criteria decision-making (MCDM) methods have been used for the risk prioritization of the failure modes of cranes.For instance, Li et al. [14] employed grey relational analysis (GRA) and fuzzy confidence theory to identify the risk of overhead cranes for metallurgical plants but did not consider the weights of O, S, and D. Raviv et al. studied dangerous situations and potential safety risks related to crane work and implemented an analytical hierarchical process (AHP) to evaluate the severity value of quantitative results, thereby calculating the total potential risk of each event.On the basis of an integrated MCDM approach combining hierarchical task analysis (HTA), the systematic human error reduction and prediction approach (SHERPA), and the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method, Mandal et al. [7] proposed a ranking method for quantifying the failure modes of human error risk in overhead crane operations.However, the risk-factor weights depend only on the subjective experience of experts, and the objective weights are ignored.Das et al. [15] created a scientific model that employed the Z-number and VIKOR methods, along with the concept of fuzzy AHP and the Shannon entropy principle, for the hazard prioritization of electric overhead traveling crane operations.To address the issue of risk management associated with the increased height of quay cranes, Zhao [16] proposed an improved FMEA approach for heightening quay cranes using entropy and GRA.By utilizing the FMEA of the construction process for heightening quay cranes as a case study to verify the effectiveness of the developed model, this study demonstrated that the method assists in reducing the impact of subjective uncertainty on risk classification and increases the precision of risk prioritization.In addition to the aforementioned MCDM technology for crane risk assessment, numerous effective and innovative methods have been widely implemented in various fields, such as complex proportional assessment (COPRAS) [17,18], the decision-making trial and evaluation laboratory (DEMATEL) technique [19], the technique for order of preference by similarity to ideal solution (TOPSIS) [20], evaluation based on distance from average solution (EDAS) [21,22], and data envelopment analysis (DEA) [23].However, research on the use of these methods for crane risk assessment is limited.
In crane risk prioritization, the subjective weights and objective weights are rarely combined.Although scholars have noted this detail and adopted the combination weighting method to determine the integrated weights of risk factors, it is challenging to rationally distribute the proportions of various weights [24].Therefore, it is necessary to develop a reasonable combination weighting approach for crane risk analysis.Methods for combination weighting have been proposed, e.g., maximizing the deviation model, maximizing the difference, the relative entropy method, the interval estimation method, mathematical programming, and the combination weighting model of game theory (CWGT).The CWGT is one of the most popular theories among these combination-weighting models and has been widely applied.However, there may be negative values of the weight coefficient after the calculation.This does not satisfy the assumption that all weight coefficients are positive.Moreover, a negative weight coefficient results in a negative weight value.This is unreasonable, because the index weight value must be >0.Fortunately, the improved combination weighting model of game theory (ICWGT) [25] proposed by Li can overcome these drawbacks.It has been applied to crane safety assessments [25] and effectiveness evaluations of electromagnetic missile launches [24].Therefore, the ICWGT was applied to determine the combination weights of O, S, and D in this study.
Although the aforementioned efforts have contributed to addressing the disadvantages of human error risk prioritization for crane operations, experts' risk attitudes are not involved in the entire risk analysis process.For addressing this issue, the MCDM method combined with prospect theory [26] has the ability to rank risk priority by reflecting the psychological behavior of experts.However, there is a critical defect in prospect theory, i.e., dominance violations.The cumulative prospect theory (CPT) [27] was developed to solve this problem and can be used for risk prioritization [28].In this study, we applied the CPT to the risk analysis of human error in crane operations.
Herein, we propose a risk prioritization model for human error in crane operations based on the CPT and ICWGT.To reflect the phenomenon where panel members have different risk attitudes toward different human errors in crane operations, CPT was applied to simulate the psychological behavior of experts.Moreover, after the subjective and objective weights of O, S, and D were determined, we established an optimization model to integrate the different weight results according to the ICWGT.Next, the final risk ranking order for each human error was determined according to the CPT and ICWGT.The remainder of this paper is organized as follows.In Section 2, the CPT and ICWGT are briefly introduced.Section 3 presents the proposed model for human error risk prioritization in crane operations.Section 4 presents a case study of the application of the proposed model.Finally, conclusions are presented in Section 5.

Cumulative prospect theory
The CPT [27] proposed by Kahneman and Tversky reflects decision-makers' subjective attitudes under risk and uncertainty.Consequently, it is used in a variety of decision-making problems in which the risk attitude of the decision-maker is considered.Cheng et al. [29] adopted fuzzy preference relations and CPT to solve the problem of international entry decisions for construction firms.Li and Zhao [30] proposed a safety assessment model based on the CPT and entropy for crane safety grade identification.Li et al. [31] developed a model based on the CPT and the Dempster-Shafer theory for trapezoidal intuitionistic fuzzy MCDM problems.
According to CPT, decision-making processes are based on the overall prospect value, which is expressed as [32] where π + (ω j ) and π -(ω j ) are decision weight functions, v ij + is a positive prospect value, and v ij is a negative prospect value.v ij + and v ij - [32] are calculated as follows:

:
where α and β are the exponent parameters, which reflect the risk attitudes of decision-makers (α = β = 0.88) [31].The parameter θ is the risk aversion coefficient (θ = 2.25) [31].4x i represents the gain or loss between x i and the reference point x o [30].
The cumulative prospect weights are determined as follows [32]: where ω j is the weight of the risk factor.γ + and γ -are risk attitude parameters and are equal to 0.61 and 0.69 [32], respectively.

Improved combination weighting model of game theory (ICWGT)
MCDM aims to support decision-makers in prioritizing alternatives related to many conflicting factors.Determining the weights of the indicators plays an important role in achieving this goal.The relative importance of each indicator is reflected in its weight [33,34].Generally, weighting methods in MCDM can be divided into three categories: subjective, objective, and combined.In the subjective weighting method, the weights of indicators are determined according to expert knowledge and experience.They are strongly affected by subjective factors, without consideration of information from objective data.In contrast, in the objective weighting method, the weights of the indices are determined using objective information regarding each index.However, objective weights are obtained directly using a mathematical method and do not involve the subjective judgments of experts.Considering the advantages and disadvantages of these two methods, scholars have proposed hybrid weighting methods that combine the strengths of both techniques while avoiding their deficiencies [35].Research on combination-weighting models is attracting increasing interest.Combination weighting methods have been proposed, such as the maximizing deviation method [36], the maximizing difference method [34], the relative entropy method [37], the interval estimation method [38], the mathematical programming method [39,40], particle swarm optimization [41], and CWGT [42] The CWGT is one of the most popular theories among these combination weighting models [43] and has been widely applied [44][45][46].However, there may be negative values of the weight coefficient after the calculation [47].This does not satisfy the assumption that all weight coefficients are positive.Although the absolute value approach was proposed to avoid negative values [47], its rationality lacks strict proof.Subsequently, the ICWGT successfully compensated for the insufficiency of the CWGT.The ICWGT procedure [25] is presented below.
Suppose that L methods are used to calculate the index weights, and L weight vectors are expressed as w l = (w l1 ,w l2 ,. ..,w ln ) (where l = 1, 2, . .., L, and n represents the number of indices).A combination weight vector w can be established as a linear combination [25]: where α l is the weight combination coefficient.
For obtaining the optimal combination weight vector, the optimization model [25] is expressed as: Then, the Lagrange function is established as follows: where λ represents the Lagrange multiplier.
After the weight coefficient a j is calculated using Eq (6), the normalized form can be expressed as: Finally, the combination weight is:

Proposed model for human error risk prioritization in crane operations
In this section, we develop a model that combines the ICWGT and CPT to prioritize human error risks in crane operations.We approach risk evaluation and ranking as an MCDM problem, with risk factors serving as evaluation indices.The proposed model is designed to rank human error risks in crane operations by considering both expert preferences and risk attitudes.First, to comprehensively evaluate and quantify the effects of various risk factors related to human error in crane operations, insights and opinions from experts in this field were sought.When reliable and precise numerical data were unavailable, linguistic variables were used to represent expert opinions.Second, given the distinct characteristics of different risk factors, it is essential to assign subjective weights to each risk factor.This is best achieved by consulting industry experts with extensive knowledge and experience in crane operations.In addition to subjective weights, objective weights can be established using entropy.To merge the subjective and objective weights in an effective and meaningful manner, the ICWGT methodology is employed to integrate subjective and objective weights.This methodology ensures that both expert opinions and objective information are considered appropriately, leading to a comprehensive and balanced assessment of the risk of human error in crane operations.Ultimately, the priority of each risk component is determined according to the overall prospect value generated through a comprehensive assessment process.The steps of the proposed approach are shown in Fig 2 and described below.

Experts' evaluation information
3.1.1.Risk evaluation for human errors of crane operations.We assume that there are i failure modes for human error in crane operations, as represented by error no i (i = 1,2,. .., n); O, S, and D, which are expressed by C j (j = 1, 2, 3); and k assessment experts, as represented by ij be the evaluation value of error no i for index C j associated with E k .Moreover, the assessment value of each error with respect to the risk factors is expressed as [7]: where e (k) ij( 1) , e (k) ij( 2) , e (k) ij (3) , and e (k) ij( 4) represent coordinates of the trapezoidal fuzzy number.
Similarly, the weight vector of the risk factor is expressed as 4) ) for the k th expert.The linguistic variables O, S, and D are presented in Tables 1-3 [7] as trapezoidal fuzzy numbers.

Aggregation of experts' language evaluation information.
For each expert, the integrated risk score is given as follows [7]: where Agg ( . ) represents the aggregation function.

Determination of subjective weights based on experts' evaluation information.
With regard to the characteristics of risk factors, subjective weights were determined according to expert experience.Similarly, using the method presented in Section 3.1.1,the weight of the risk factor is expressed as 4) ) for the k th expert.The where e ij denotes the defuzzified trapezoidal fuzzy information of the j th risk factor with respect to error no i .
Step 2: Determine entropy weight of risk factors After the decision matrix of the failure modes is obtained, the weights O, S, and D are determined according to the entropy weight method.The entropy weight is calculated as follows [48]: The information entropy of each risk factor is expressed as: where μ ji denotes the projection value of human error evaluation information.To ensure that μ ji lnμ ji has mathematical meaning, μ ji lnμ ji is defined as 0 when μ ji = 0. μ ji can be calculated as: The entropy weight of each risk factor is expressed as: Table 4. Linguistic variables for the weights of risk factors [7].

Computation of combination weight.
Let w 1 and w 2 denote the subjective and objective weight vectors, respectively.The combination weight calculated via the ICWGT is denoted as w (ICWGT) , which is combined using Eqs (7) and (8).

Rank risk priority of human error based on CPT
3.3.1.Normalize decision-making matrix.To better reflect the gains and losses in prospect theory, it is necessary to normalize the decision-making matrix e = (e ij ).The normalized values of the benefit-and cost-related indices were calculated as follows [49]: For the cost index, e ij can be normalized as: For the beneficial index, e ij can be normalized as: Here, max j ðe ij Þ represents the maximum performance rating among the human errors for the i th risk factor, and min j ðe ij Þ represents the minimum performance rating among the human errors for the i th risk factor.
The normalized decision-making matrix R is expressed as: In this study, risk factors (O, S, and D) were used as cost indices [50].

Determine positive ideal and negative ideal solutions.
When making a decision based on prospect theory, decision-makers typically evaluate the gains and losses of alternatives according to reference points.In this study, the positive ideal solution (PIS) and negative ideal solution (NIS) were considered as the reference points [51][52][53] Using Eq (2), the positive prospect value matrix is established as: The negative prospect value matrix is obtained as: ; ð24Þ where i = 1, 2, . .., n; j = 1, 2, . .., m; and v ij -= -2.25(r j + -r ij ) 0.88 .3.3.4.Determine risk priority order of human errors in crane operations.The integrated prospect value V i for the failure modes of human error was calculated using Eq (1).Human error risk prioritization was calculated by ranking V i for each error.

Case study
The proposed model was applied to prioritize human error risk in overhead crane operations.Next, we conducted a comparative study and sensitivity analysis to verify the effectiveness of the method described above.The results of the risk prioritization provide valuable guidance for safety management departments.The proposed model framework is implemented for human error risk prioritization in crane operations using the following steps:

Determine human errors and collect experts' evaluation data
Overhead cranes are widely used in industrial and mining enterprises and can easily fail because of human error during operations.The determination of human errors during overhead crane operations plays an important role in the proposed model.As shown in Table 5, 21 Check omitted (bridge) Check omitted/incomplete (sling and all other lifting accessories for damage) Check omitted/incomplete (sling and all other lifting accessories for load limit) Check omitted (load limit of hoist rope) Misalign (the beam is not properly tied to the hook while loading) Misalign (Belt is not tied around the hardware (load) properly) Misalign (Hardware is not attached to beam by belt properly) Wrong selection made (Wrong pendant push button pressed while operating the crane) Misalign (Hardware not smoothly placed on the vehicle) Information not obtained (Information about the position to lower the hardware not received) Information not communicated (Information about the position to lower the hardware not communicated) Wrong information obtained (Wrong information about the position to lower the hardware received) Wrong information communicated (Wrong information about the position to lower the hardware communicated) https://doi.org/10.1371/journal.pone.0297120.t005human errors were identified [7], which are denoted as error no i (i = 1, 2, . .., 21).Each error was evaluated according to the three risk factors (O, S, and D) presented in Tables 1-3 [7].In this case, four experts E 1 , E 2 , E 3 , E 4 evaluated the human errors with regard to O, S, and D. The evaluation results for each error with regard to O, S, and D and the weights of O, S, and D are presented in Table 6 [7].

Integration and defuzzification of evaluation information of human error
To rank the risk prioritization of human errors, the experts' linguistic evaluation information for O, S, and D is integrated, and their weights are converted into trapezoidal fuzzy numbers using Eqs ( 11)-( 14) and then defuzzified to crisp values using Eq (15).The results of the integration and defuzzification are presented in Table 7 [7].

Calculation of combination weights
To reflect the potential information of evaluation data, the entropy weight method is adopted to calculate the weights of O, S, and D. According to Table 7, μ ji can be obtained, as shown in Table 8.Considering the data provided in Table 7, Eqs ( 17) and ( 19) are used to determine the objective weight.The normalized subjective weights of O, S, and D are then calculated, and they are presented in Table 9. Next, the integrated weights are calculated using Eqs (7) and (8) according to the ICWGT.The values for the three different types of weights (O, S, and D) are presented in Table 9. Fig 3 shows that the integrated weights calculated via the ICWGT are the optimal equilibrium values between the other two.

Determination of positive and negative prospect matrices
According to Table 8 and Eqs ( 20) and ( 21), the normalized decision matrix is obtained as:

Rank human error risk prioritization in overhead crane operations
According to the overall prospect values calculated using Eq (5), the risk prioritization of all the errors is as follows: error 11 > error 12> error 7 > error 15 > error 16 > error 13 = error 14 > error 10 > error 9 > error 6 > error 3 > error 5 > error > error 2 > error 8 > error 17 > error 20 > error 18 = error 21 > error 19 > error 1.Clearly, error 11 has the highest risk priority and deserves focus on preventive measures, whereas error 1 has the lowest relative risk.The ranking of the errors is presented in Table 10.This can help risk managers identify the key points in overhead crane safety management and would be advantageous in formulating reasonable suggestions.Comparative and sensitivity analyses were performed, and the results are shown in Figs 4 and 5, respectively.

Sensitivity analysis
To verify the robustness of the proposed model and examine the influence of associated parameters on human error risk prioritization in overhead crane operations, a sensitivity analysis was conducted using the Kingsoft Office software WPS.This method involves examining a single parameter at a time while assuming that θ, α, and β are independent of each other; that is, only one parameter is changed at a time, while the other parameters remain constant, to analyze its influence on the results.Using the WPS software, various scenarios and simulations can be performed to determine how changes in the parameters affect the overall outcome.In view of the CPT, the risk preferences for determining the risk prioritization are reflected by the parameters θ, α, and β in Eq (1).The value of θ (risk aversion coefficient) is >1.For a higher prospect value, the decision-maker is more sensitive to risk.In the gain interval, α represents the degree of concavity of the value function.In the loss interval, β represents the degree of convexity of the value function.For higher values of α and β, the decision-maker is less likely to avoid risk.To analyze the effect of each risk preference coefficient on the decision outcomes, we established three dynamic scenarios [54] by systematically adjusting the risk parameters.The results fluctuated for errors 2 and 8, indicating that they are vulnerable to the influence of θ.However, other error ranks remained unchanged.For example, errors 11 and 1 maintained the highest and lowest risk, respectively.Thus, the general trend of risk prioritization remained nearly unchanged, with high rank stability.The other human error risk rankings remained the same, indicating that the proposed framework is relatively stable.

Comparison analysis
The first comparative analysis was conducted between the proposed method and the RPN of traditional FMEA.When the RPN was used to rank the risk prioritization of human error in overhead crane operations, the risk order of the 21 13 were not consistent between the RPN and the proposed method, whereas the other prioritizations were the same.The main reason for this is that the proposed method can address the disadvantages of the RPN of traditional FMEA mentioned in Section 1.The proposed method ranks human error risk prioritization according to overall prospect values.In addition, the ICWGT was applied to the proposed FMEA framework by considering the rationality of the risk-factor weight aggregation.In this case study, the proposed method and RPN produced similar ranking results, indicating the effectiveness of these approaches.However, it is important to note that use of the RPN may not always be suitable in practical scenarios.For instance, let us consider the representation of errors as (O = 6, S = 5, D = 7), (O = 6, S = 7, D = 5), and (O = 5, S = 6, D = 7), all of which have RPN scores of 210.It is evident that relying solely on RPN scores does not offer a meaningful basis for comparing the risks associated with these errors.In contrast, the proposed method, which incorporates weights and considers the decision-makers' risk attitudes, can effectively address such situations.Thus, the risk prioritization determined via the proposed method has advantages over the RPN of traditional FMEA.To further verify the applicability and efficiency of the proposed model, another comparative analysis was performed using Mandal's method [7] and VIKOR.The results are shown in Fig 5 .The second comparison was conducted using Mandal's study [7], in which the VIKOR technique was applied to the aforementioned case.We also ranked the 21 errors using VIKOR.From Table 10 and Fig 5, the value of Q i was significantly different from that reported in the literature [7].For example, if O and S are taken as cost indices and D is taken as a benefit index, the risk priority index Q 1 for Error 1 is calculated using VIKOR as follows: where S* = 0.341707, S − = 1.207565,R* = 0.216667, R − = 0.73, v = 0.5, S 1 = 0.820683, and R 1 = 0.53.
If O, S, and D are all considered as cost indices, the risk priority index Q 1 for error 1 is calculated using VIKOR as follows: The calculated values of S*, S − , R*, R − , S 1 , and R 1 were 0.2907, 1.7133, 0.2167, 0.73, 0.2907, 0.2578, respectively, for VIKOR.In both situations, the value of Q 1 (Q 1 = 0.581785 or 0.0401) differs from that (Q 1 = 0.675342 [7]) obtained in Mandal's study.This may be due to calculation errors in the previous study [7].In the present study, O, S, and D were all considered as cost indices [50], and the other results of Q i were calculated and are presented in column 6 of Table 10.
A third comparison was conducted between the proposed method and VIKOR.As shown in Fig 5, the risk priorities for human error obtained using the proposed method and VIKOR were different.Although the prioritization results are not completely consistent, error 11 always had a higher risk priority than the others in this case, indicating the effectiveness and  10, the prospect value interval and priority order range obtained via the proposed method were [-2.0148, 0.5196] and 1-19, respectively, which were wider than those of the VIKOR method.This indicates that the proposed framework is effective for ranking human error risk prioritization in crane operations.The differences in the prioritization results obtained via the proposed method and VIKOR are primarily attributed to their distinct mechanisms for prioritizing human error risk in overhead crane operations.The VIKOR method uses the risk value Q to rank the risk priorities of human error, whereas the proposed method ranks risk priorities according to overall prospect values, which can reflect the experts' risk attitude and psychological behavior.VIKOR considers only the subjective weights of the risk factors, whereas the proposed method involves integration weights combined with ICWGT.Therefore, the risk prioritization results obtained using the proposed method are more rational and practical than those obtained using VIKOR.

Summary
Considering the shortcomings of existing methods, we propose a model for human error risk prioritization in crane operations based on the ICWGT and CPT.To address the uncertainty in risk assessment related to human error, trapezoidal fuzzy numbers are employed to describe the risk information.Subsequently, the entropy weighting method is used to calculate the objective weights of the three risk factors.The ICWGT is applied to combine the subjective and objective weights.Furthermore, a ranking mechanism based on the CPT was established for evaluating human error risks in crane operations.The overall prospect value is adopted to determine the risk ranking.Finally, a case study involving human error risk priority in overhead crane operations was conducted to validate the proposed method.A comparative analysis indicated that the proposed method can reasonably prioritize human error risk in crane operations.
The key accomplishments and contributions of this study are summarized as follows.First, a risk priority model for human errors in crane operations based on the ICWGT and CPT was developed.Second, the extended FMEA model incorporating the CPT considers experts' risk attitudes and decision psychology, resulting in a relatively objective and rational risk priority ranking.Third, in the ICWGT combination weighting method, reasonable weights are obtained by separately determining the subjective and objective weights of O, S, and D. The proposed model may be applicable to risk assessments in other industries.

Limitations of study
The proposed method, which incorporates the CPT and ICWGT for human error risk prioritization in crane operations, has limitations.(1) In the risk assessment process, the experts' attitudes toward risk are dynamic.This implies that different experts may have different attitudes toward risk, which can vary over time.However, the proposed model neglects the dynamic nature of expert opinions during the evaluation process by assuming that the viewpoints of the experts remain unchanged.Consequently, further research is needed to explore the dynamic risk attitudes of experts throughout the assessment process.(2) The proposed method does not consider the potential influence of leaders or experts who may have special connections within the organization.These individuals may have a significant impact on the risk attitudes of experts.Future research should consider the role of these influential figures and explore the extent to which their connections affect experts' attitudes toward risk.(3) Importantly, the results presented in this paper were obtained from a limited set of case data.Further practical studies are needed to confirm the feasibility and effectiveness of the proposed model.Future research can help verify the applicability of the proposed model across different contexts and provide a more comprehensive understanding of its potential benefits.

Proposed further research
Future studies should explore the following avenues.First, the linguistic evaluation information provided by different team members regarding the risk factors must be aggregated by considering the members' weights.Second, it may be necessary to not only rank the human error risks of crane operations but also determine their risk grades.Third, hesitant fuzzy sets, spherical fuzzy sets, Pythagorean fuzzy sets, and Z-numbers should be explored to capture experts' evaluation information more reliably and comprehensively.

( 1 ) 4 . 6 . 1 .
In dynamic scenario I, the coefficients α and β remained constant while the parameter θ was varied from 1 to 10. (2) In dynamic scenario II, the coefficients θ and β remained constant while the parameter α was varied from 0 to 1. (3) In dynamic scenario III, the coefficients θ and α remained constant while the parameter β was varied from 0 to 1.Control parameter θ.Taking θ = 1, 3, 5, 7, and 9, respectively, with the other parameters constant, the results of human error risk prioritization are presented in Fig 4. As shown, changes in the risk aversion coefficient θ affect the risk prioritization of human errors.